Abstract

The time-resolved photoluminescence in Rhodamine B dye embedded in aqueous suspensions of polystyrene spheres shows an anomalous fast nonexponential decay in addition to the slow decay that is intrinsic to dye molecules. When the volume fraction of spheres is increased to a critical value, the relative intensity of the fast component increases while the decay rate remains constant at 15 ps. A further increase of the volume fraction lengthens the lifetime of this component to the order of 1 ns. The quantitative behavior of the time dependence of the luminescence is explained well when we consider that dye molecules are adsorbed two dimensionally upon spheres and that the fast decay originates in the resonance energy transfer between the dye molecules.

© 1999 Optical Society of America

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References

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  1. P. W. Barber and R. K. Chang, eds., Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).
  2. R. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
  3. C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
    [CrossRef]
  4. H. M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984).
    [CrossRef] [PubMed]
  5. H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, “Some characteristics of a droplet whispering-gallery-mode laser,” Opt. Lett. 11, 614–616 (1986).
    [CrossRef] [PubMed]
  6. M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
    [CrossRef]
  7. A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
    [CrossRef] [PubMed]
  8. L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
    [CrossRef]
  9. S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987).
    [CrossRef]
  10. H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
    [CrossRef] [PubMed]
  11. S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990); “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12778 (1991).
    [CrossRef] [PubMed]
  12. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  13. G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
    [CrossRef] [PubMed]
  14. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
    [CrossRef]
  15. J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1880 (1990); W. L. Vos, R. Sprik, A. van Blaaderen, A. Imhof, A. Largendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16, 231–16, 235 (1996); W. L. Vos, M. Megens, C. M. van Kats, and P. Bosecke, “Transmission and diffraction by photonic colloidal crystals,” J. Phys.: Condens. Matter JCOMEL 8, 9503–9507 (1996).
    [CrossRef] [PubMed]
  16. J. Martorell and N. M. Lawandy, “Spontaneous emission in a disordered dielectric medium,” Phys. Rev. Lett. 66, 887–890 (1991).
    [CrossRef] [PubMed]
  17. B. Y. Tong, P. K. John, Y. Zhu, Y. S. Liu, S. K. Wong, and W. R. Ware, “Fluorescence-lifetime measurements in monodispersed suspensions of polystyrene particles,” J. Opt. Soc. Am. B 10, 356–359 (1993); N. M. Lawandy, “Fluorescence-lifetime measurements in monodispersed suspensions of polystyrene particles: comment,” J. Opt. Soc. Am. B 10, 2144–2146 (1993); A. Imhof, M. Megens, J. J. Engelberts, D. T. N. de Lang, R. Sprik, and W. L. Vos, “Spectroscopy of fluorescein (FITC) dyed colloidal silica spheres,” J. Phys. Chem. B JPCBFK 103, 1408–1415 (1999).
    [CrossRef]
  18. T. Kuge, “Application of polymers to clinical analyses,” Funct. Mater. 2, 56–65 (1983; in Japanese).
  19. T. For¨ster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc. 27, 7–17 (1959).
    [CrossRef]
  20. K. B. Eisenthal and S. Siegel, “Influence of resonance transfer on luminescence decay,” J. Chem. Phys. 41, 652–655 (1964).
    [CrossRef]
  21. R. G. Bennett, “Radiationless intermolecular energy transfer,” J. Chem. Phys. 41, 3037–3040 (1964).
    [CrossRef]
  22. M. Tomita and K. Totsuka, “Resonance energy transfer and laser actions in strongly scattering optical media,” Prog. Cryst. Growth Charact. Mater. 33, 351–354 (1996).
    [CrossRef]
  23. F. P. Schfer, ed., Dye Lasers (Springer-Verlag, Berlin, 1977); I. D. Rattee and M. M. Breuer, eds., The Physical Chemistry of Dye Adsorption (Academic, New York, 1974).
  24. M. Tomita, K. Ohosumi, and H. Ikari, “Enhancement of molecular interactions in strongly scattering dielectric composite optical media,” Phys. Rev. B 50, 10369–10372 (1994).
    [CrossRef]
  25. Polysciences, Inc. 400 Valley Road, Warrington, Pa. 18976.

1996 (1)

M. Tomita and K. Totsuka, “Resonance energy transfer and laser actions in strongly scattering optical media,” Prog. Cryst. Growth Charact. Mater. 33, 351–354 (1996).
[CrossRef]

1994 (2)

M. Tomita, K. Ohosumi, and H. Ikari, “Enhancement of molecular interactions in strongly scattering dielectric composite optical media,” Phys. Rev. B 50, 10369–10372 (1994).
[CrossRef]

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

1992 (1)

M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
[CrossRef]

1991 (2)

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

J. Martorell and N. M. Lawandy, “Spontaneous emission in a disordered dielectric medium,” Phys. Rev. Lett. 66, 887–890 (1991).
[CrossRef] [PubMed]

1988 (2)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

1987 (2)

S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

1986 (1)

1985 (1)

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

1984 (1)

1983 (1)

T. Kuge, “Application of polymers to clinical analyses,” Funct. Mater. 2, 56–65 (1983; in Japanese).

1964 (2)

K. B. Eisenthal and S. Siegel, “Influence of resonance transfer on luminescence decay,” J. Chem. Phys. 41, 652–655 (1964).
[CrossRef]

R. G. Bennett, “Radiationless intermolecular energy transfer,” J. Chem. Phys. 41, 3037–3040 (1964).
[CrossRef]

1961 (1)

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[CrossRef]

1959 (1)

T. For¨ster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc. 27, 7–17 (1959).
[CrossRef]

Arnold, S.

S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987).
[CrossRef]

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

Bennett, R. G.

R. G. Bennett, “Radiationless intermolecular energy transfer,” J. Chem. Phys. 41, 3037–3040 (1964).
[CrossRef]

Bond, W. L.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[CrossRef]

Campillo, A. J.

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, “Some characteristics of a droplet whispering-gallery-mode laser,” Opt. Lett. 11, 614–616 (1986).
[CrossRef] [PubMed]

Chang, R. K.

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

Druger, S. D.

S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987).
[CrossRef]

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

Eisenthal, K. B.

K. B. Eisenthal and S. Siegel, “Influence of resonance transfer on luminescence decay,” J. Chem. Phys. 41, 652–655 (1964).
[CrossRef]

Ema, K.

M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
[CrossRef]

Eversole, J. D.

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Folan, L. M.

S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987).
[CrossRef]

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

For¨ster, T.

T. For¨ster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc. 27, 7–17 (1959).
[CrossRef]

Garrett, C. G. B.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[CrossRef]

Genack, A. Z.

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

Huston, A. L.

Ikari, H.

M. Tomita, K. Ohosumi, and H. Ikari, “Enhancement of molecular interactions in strongly scattering dielectric composite optical media,” Phys. Rev. B 50, 10369–10372 (1994).
[CrossRef]

Justus, B. L.

Kaiser, W.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[CrossRef]

Kuge, T.

T. Kuge, “Application of polymers to clinical analyses,” Funct. Mater. 2, 56–65 (1983; in Japanese).

Kurizki, G.

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

Kuwata-Gonokami, M.

M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
[CrossRef]

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

J. Martorell and N. M. Lawandy, “Spontaneous emission in a disordered dielectric medium,” Phys. Rev. Lett. 66, 887–890 (1991).
[CrossRef] [PubMed]

Lin, H.-B.

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, “Some characteristics of a droplet whispering-gallery-mode laser,” Opt. Lett. 11, 614–616 (1986).
[CrossRef] [PubMed]

Long, M. B.

Martorell, J.

J. Martorell and N. M. Lawandy, “Spontaneous emission in a disordered dielectric medium,” Phys. Rev. Lett. 66, 887–890 (1991).
[CrossRef] [PubMed]

Ohosumi, K.

M. Tomita, K. Ohosumi, and H. Ikari, “Enhancement of molecular interactions in strongly scattering dielectric composite optical media,” Phys. Rev. B 50, 10369–10372 (1994).
[CrossRef]

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

Siegel, S.

K. B. Eisenthal and S. Siegel, “Influence of resonance transfer on luminescence decay,” J. Chem. Phys. 41, 652–655 (1964).
[CrossRef]

Takeda, K.

M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
[CrossRef]

Tomita, M.

M. Tomita and K. Totsuka, “Resonance energy transfer and laser actions in strongly scattering optical media,” Prog. Cryst. Growth Charact. Mater. 33, 351–354 (1996).
[CrossRef]

M. Tomita, K. Ohosumi, and H. Ikari, “Enhancement of molecular interactions in strongly scattering dielectric composite optical media,” Phys. Rev. B 50, 10369–10372 (1994).
[CrossRef]

Totsuka, K.

M. Tomita and K. Totsuka, “Resonance energy transfer and laser actions in strongly scattering optical media,” Prog. Cryst. Growth Charact. Mater. 33, 351–354 (1996).
[CrossRef]

Tzeng, H. M.

Wall, K. F.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yasuda, H.

M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
[CrossRef]

Chem. Phys. Lett. (1)

L. M. Folan, S. Arnold, and S. D. Druger, “Enhanced energy transfer within a microparticle,” Chem. Phys. Lett. 118, 322–327 (1985).
[CrossRef]

Discuss. Faraday Soc. (1)

T. For¨ster, “Transfer mechanisms of electronic excitation,” Discuss. Faraday Soc. 27, 7–17 (1959).
[CrossRef]

Funct. Mater. (1)

T. Kuge, “Application of polymers to clinical analyses,” Funct. Mater. 2, 56–65 (1983; in Japanese).

J. Chem. Phys. (3)

K. B. Eisenthal and S. Siegel, “Influence of resonance transfer on luminescence decay,” J. Chem. Phys. 41, 652–655 (1964).
[CrossRef]

R. G. Bennett, “Radiationless intermolecular energy transfer,” J. Chem. Phys. 41, 3037–3040 (1964).
[CrossRef]

S. D. Druger, S. Arnold, and L. M. Folan, “Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles,” J. Chem. Phys. 87, 2649–2659 (1987).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

M. Kuwata-Gonokami, K. Takeda, H. Yasuda, and K. Ema, “Laser emission from dye-doped polystyrene microsphere,” Jpn. J. Appl. Phys., Part 1 32, L99–L101 (1992).
[CrossRef]

Nature (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124, 1807–1809 (1961).
[CrossRef]

Phys. Rev. A (1)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

Phys. Rev. B (1)

M. Tomita, K. Ohosumi, and H. Ikari, “Enhancement of molecular interactions in strongly scattering dielectric composite optical media,” Phys. Rev. B 50, 10369–10372 (1994).
[CrossRef]

Phys. Rev. Lett. (4)

A. J. Campillo, J. D. Eversole, and H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
[CrossRef] [PubMed]

J. Martorell and N. M. Lawandy, “Spontaneous emission in a disordered dielectric medium,” Phys. Rev. Lett. 66, 887–890 (1991).
[CrossRef] [PubMed]

Prog. Cryst. Growth Charact. Mater. (1)

M. Tomita and K. Totsuka, “Resonance energy transfer and laser actions in strongly scattering optical media,” Prog. Cryst. Growth Charact. Mater. 33, 351–354 (1996).
[CrossRef]

Other (7)

F. P. Schfer, ed., Dye Lasers (Springer-Verlag, Berlin, 1977); I. D. Rattee and M. M. Breuer, eds., The Physical Chemistry of Dye Adsorption (Academic, New York, 1974).

B. Y. Tong, P. K. John, Y. Zhu, Y. S. Liu, S. K. Wong, and W. R. Ware, “Fluorescence-lifetime measurements in monodispersed suspensions of polystyrene particles,” J. Opt. Soc. Am. B 10, 356–359 (1993); N. M. Lawandy, “Fluorescence-lifetime measurements in monodispersed suspensions of polystyrene particles: comment,” J. Opt. Soc. Am. B 10, 2144–2146 (1993); A. Imhof, M. Megens, J. J. Engelberts, D. T. N. de Lang, R. Sprik, and W. L. Vos, “Spectroscopy of fluorescein (FITC) dyed colloidal silica spheres,” J. Phys. Chem. B JPCBFK 103, 1408–1415 (1999).
[CrossRef]

J. Martorell and N. M. Lawandy, “Observation of inhibited spontaneous emission in a periodic dielectric structure,” Phys. Rev. Lett. 65, 1877–1880 (1990); W. L. Vos, R. Sprik, A. van Blaaderen, A. Imhof, A. Largendijk, and G. H. Wegdam, “Strong effects of photonic band structures on the diffraction of colloidal crystals,” Phys. Rev. B 53, 16, 231–16, 235 (1996); W. L. Vos, M. Megens, C. M. van Kats, and P. Bosecke, “Transmission and diffraction by photonic colloidal crystals,” J. Phys.: Condens. Matter JCOMEL 8, 9503–9507 (1996).
[CrossRef] [PubMed]

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990); “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12778 (1991).
[CrossRef] [PubMed]

Polysciences, Inc. 400 Valley Road, Warrington, Pa. 18976.

P. W. Barber and R. K. Chang, eds., Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).

R. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).

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Figures (6)

Fig. 1
Fig. 1

Time dependence of luminescence for Rhodamine B at 10-3 mol/l in aqueous suspensions of polystyrene spheres of 0.12-µm diameter. The volume fractions of the spheres are (a) 9%, (b) 5.1%, (c) 3.6%, (d) 2.5%, (e) 2.1%, (f) 1.7%, (g) 1.3%, (h) 1.2%, and (i) 0.7%.

Fig. 2
Fig. 2

Solid curve, time dependence of photoluminescence for Rhodamine B at 10-3 mol/l in aqueous suspensions of polystyrene spheres 0.12 µm in diameter. The volume fraction is 1.7%. Dashed curve, time dependence of the reflected excitation light.

Fig. 3
Fig. 3

Time dependence of luminescence for a pure Rhodamine B aqueous solution. The concentrations are (a) 1.0×10-5, (b) 3.0×10-3, (c) 5.2×10-3, (d) 8.3×10-3, (e) 1.4×10-2, and (f) 4.2×10-2 mol/l.

Fig. 4
Fig. 4

Time dependence of luminescence for Rhodamine B at 10-3 mol/l in aqueous suspensions of polystyrene spheres. (a) Diameter, 0.45 µm; volume fractions of the spheres are (a) 9%, (b) 6.6%, (c) 5.8%, (d) 4.5%, (e) 3.3%, (f) 1.8%. (b) Diameter, 1.026 µm; volume fractions of the spheres are (a) 9.0%, (b) 6.7%, (c) 3.6%.

Fig. 5
Fig. 5

Solid and dashed curves, calculated curves of [NA]/N0 and [NA]/S0, respectively, as functions of sphere density on the basis of Eqs. (5). k=κ/N0=1, 10, 100.

Fig. 6
Fig. 6

Filled circles, ratios of intensity of the fast-decay component to the total intensity of the luminescence at t=0; open circles and open squares, normalized decay rates γ2 and γ3 as functions of the volume fraction calculated on the basis of Eq. (1) with m=2 and m=3, respectively. Solid and dashed curves, calculated curves of [NA]/N0 and [NA]/S0, respectively, on the basis of Eqs. (5). k=κ/N0=1000.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Im(t)=I0 exp[-t/τ-γm(t/τ)6/m],
γm=Γ[1-(m/6)](NA/Rv)mR0m.
R0=3c4bbA26/mπ(ε/ε0)20fa(w)fb(w)w4dw1/6,
bb=wπ|M|23cε2
Im(t)=exp[-(t/τ)]{(1-α)+α exp[-γm(t/τ0)6/m]},
[NA]=κ[S][NF],
N0=[NA]+[NF],
S0=[NA]+[S],

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